Question

y^3+2xy=5 find dy/dx ​

Answer 1

$\huge \mathfrak{solution}$

$\boxed{ \bold{ {y}^{3} + 2xy = 5}}$

Differentiate both side w.r.t X

$\implies \: \frac{d}{dx} ({y}^{3} + 2xy) = \frac{d}{dx} (5) \\ \\ \implies \: 3 {y}^{3 - 1} \frac{dy}{dx} + 2(x \frac{dy}{dx} + y) = 0 \\ \\ \implies \: 3 {y}^{2} \frac{dy}{dx} + 2x \frac{dy}{dx} + 2y = 0 \\ \\ \implies \: (3 {y}^{2} + 2x) \frac{dy}{dx} = - 2y \\ \\ \implies \: \frac{dy}{dx} = \boxed{\bold{ \pink{\frac{ - 2y}{3 {y}^{2} + 2x } }}}$

Formula used :

$\star \: \boxed{ \red{ \bold{\frac{d}{dx} {x}^{n} = n {x}^{n - 1} }}}$

$\star \boxed{ \bold{ \red{\frac{d}{dx} (u.v) = u \: \frac{dv}{dx} + v \: \frac{du}{dx} }}}$